Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist

The paper provides a thorough review of the state-of-the-art theory calculations for LHC applications and lists the key developments needed to match the ever increasing experimental precision. It will serve as a very useful reference for the HEP community and an indicator of the next key directions. I find that the paper fully meets the SciPost Physics Community Reports Acceptance Criteria and recommend it to be published after a minor revision.

General comments:

1) The review claims to point out areas where progress is needed in order to match the experimental precision, "... we indicate processes and missing higher-order corrections that are required to reach the theoretical accuracy that matches the anticipated experimental precision.". For most processes in Section 3, the anticipated experimental precision (current and HL-LHC) is clearly laid out, and where experimental precision surpasses the theory precision, the case is compelling. However, for a handful of channels the rationale for targeting additional higher-order corrections is not spelled out. To help readers appreciate the theoretical challenges in the "desired" precision, it would be useful to briefly discuss, for each of the following, why existing calculations fall short of projected experimental uncertainties: - HH+2j - tH - bbH - V+bb - VV+j - yy, yy+>=1j, yyy - ttj - tt+>=2j - tt+bb - tZj

2) 2.1 Parton distribution functions "It is encouraged to use NLO QCD (or even NNLO QCD) PDFs where possible, even for computation of lower perturbative accuracy" -> Naively it seems that using a consistent setup might be better (e.g. NLO PDFs with NLO calculations). Do comparisons with data show that taking the NNLO PDFs is always better than NLO? I suggest clarifying this point or provide additional information for the readers.

3) 2.1 Parton distribution functions, 2nd paragraph -> References for PDF sets are not provided (CT18, MSHT20, NNPDF3.1/4.0). Perhaps that's fine because you cite PDF4LHC21. However, in that case consider citing PDF4LHC15 for consistency or provide a reference for each PDF set. Preferably, everything would be properly cited.

4) Page 13, Jet algorithms, identified final states, and fragmentation -> The section discusses several cases of mismatch between theory and experiment (or fixed-order vs ME + PS). Another issue, not mentioned here, is the mismatch between the "particle-level" observables and "parton-level" observables, which are particularly important for measurements with jets (e.g. discussed briefly in 2506.13449, Figure 1). I suggest mentioning this as another source of uncertainty, which must be addressed when we compare e.g. V+HF measurements to fixed-order calculations or for their inclusion in global PDF fits.

5) Section 3.1 Higgs boson associated processes -> In this section you often refer to ATLAS analyses for the state-of-the-art experimental precision. However, CMS results with similar precision are sometimes not mentioned. I think it would be better to cite results from both collaborations where appropriate. For example, ATLAS references without a matching CMS reference are [511], [536], [555], [556], [608], and possibly others.

6) Page 19, last paragraph "If the remaining systematic errors (dominated for the diphoton analysis by the spurious signal systematic error) remain the same, the resultant systematic error would be of the order of 9%, leading to a total error of approximately 9.5%." -> Experiments will likely find a way to deal with the spurious signal systematic uncertainty and reduce it such that it will be more comparable to the statistical uncertainty. Would that change any of the conclusions on what calculations are needed? Please explain in the text if it's relevant.

1) Address the general comments from the Report

2) Page 4, 1st paragraph -> Capitalize "ploughshare"

3) Page 4, last paragraph "... as for example in the Higgs Cross Section Working Group. (See the discussion on approximate N3LO PDFs below.)" -> Should this rather be formatted as "... as for example in the Higgs Cross Section Working Group (see the discussion on approximate N3LO PDFs below)."?

4) Page 6, 3rd paragraph "There are sizeable differences in the gg PDF luminosity not observed in the qq PDF luminosity." -> Suggest clarifying what differences exactly you mean. In both cases the blue and green curves do not agree within the uncertainty bands shown at around 100 - 200 GeV.

5) Page 6, 3rd paragraph "... and then to take the ratio of the two ratios, as shown in Figure 2." -> Figure 2 does not seem to show a double-ratio as specified in the text. It just shows the ratio of aN3LO to NNLO PDFs. Please correct appropriately.

6) Figure 1 right -> There are spikes in the error bands, most notably in the green curve at 500 GeV. Are these just numerical issues that could be fixed?

7) Page 12, Electroweak corrections, 1st paragraph "run III of the LHC" -> The official name of the 3rd run is "Run 3", not "run III". Please change appropriately throughout the text (e.g. also on page 32, possibly others).

8) Page 12, Electroweak corrections, 2nd and 3rd paragraph -> Repetitive use of the word "plethora", consider rephrasing one of the sentences.

9) Section 3.1 Higgs boson associated processes -> It might be better to drop the reference to Table 2 in this section and include it only in Section 3.1.2 Production. This would also solve the ordering issue where Table 2 is referenced before Table 1.

10) Section 3.1.1 Higgs Decays -> Suggest stating whether the current precision in partial width calculations is sufficient or if higher-order calculations are needed (e.g. for HL-LHC). This would be similar to the "known" / "desired" format in the following.

11) Page 20, first paragraph, last sentence -> Capitalize "standard model" here and elsewhere

12) Page 23, last paragraph -> Suggest stating whether the "known" and "desired" theory calculations will be precise enough for this data.

Ask for minor revision